MOTION MOUNTAIN part III ppt

Curiosityabout how people, animals, things, images and space move leads to many adventures.This volume presents the adventures one encounters when exploring everything electric.The story

MOTION MOUNTAIN the adventure of physics – vol.iii

light, charges and brains

www.motionmountain.net

Motion Mountain

The Adventure of Physics Volume III

Light, Charges and Brains

Edition 25.30, available as free pdf atwww.motionmountain.net

Proprietas scriptoris © Chrestophori Schiller

primo anno Olympiadis trigesimae.

Omnia proprietatis iura reservantur et vindicantur.

Imitatio prohibita sine auctoris permissione.

Non licet pecuniam expetere pro aliqua, quae

partem horum verborum continet; liber

pro omnibus semper gratuitus erat et manet.

Twenty-fifth edition.

Copyright © 2012 by Christoph Schiller,

the first year of the 30th Olympiad.

This pdf file is licensed under the Creative Commons

Attribution-Noncommercial-No Derivative Works 3.0 Germany Licence, whose full text can be found on the website

creativecommons.org/licenses/by-nc-nd/3.0/de ,

with the additional restriction that reproduction, distribution and use,

in whole or in part, in any product or service, be it

commercial or not, is not allowed without the written consent of the copyright owner The pdf file was and remains free for everybody

to read, store and print for personal use, and to distribute

electronically, but only in unmodified form and at no charge.

τῷ ἐμοὶ δαὶμονι

“Primum movere, deinde docere *

”

Antiquity

This book is written for anybody who is curious about nature and motion Curiosityabout how people, animals, things, images and space move leads to many adventures.This volume presents the adventures one encounters when exploring everything electric.The story ranges from the weighing of electric current to the use of magnetic fields toheal bone fractures and up to the understanding of the human brain

In the structure of physics, shown inFigure 1, motion due to electricity is the mostfascinating aspect of the starting point at the bottom Indeed, almost everything around

us is due to electric processes The present introduction to electricity, magnetism, lightand the brain is the third of a six-volume overview of physics that arose from a threefoldaim that I have pursued since 1990: to present motion in a way that is simple, up to dateand captivating

In order to be simple, the text focuses on concepts, while keeping mathematics to the

necessary minimum Understanding the concepts of physics is given precedence overusing formulae in calculations The whole text is within the reach of an undergraduate

In order to be up to date, the text is enriched by the many gems – both theoretical and

empirical – that are scattered throughout the scientific literature

In order to be captivating, the text tries to startle the reader as much as possible

Read-ing a book on general physics should be like goRead-ing to a magic show We watch, we areastonished, we do not believe our eyes, we think, and finally we understand the trick.When we look at nature, we often have the same experience Indeed, every page presents

at least one surprise or provocation for the reader to think about Numerous interestingchallenges are proposed

The motto of the text, die Menschen stärken, die Sachen klären, a famous statement by

Hartmut von Hentig on pedagogy, translates as: ‘To fortify people, to clarify things.’ ifying things – and adhering only to the truth – requires courage, as changing the habits

Clar-of thought produces fear, Clar-often hidden by anger But by overcoming our fears we grow

in strength And we experience intense and beautiful emotions All great adventures inlife allow this, and exploring motion is one of them Enjoy it!

Munich, 1 November 2012

* ‘First move, then teach.’ In modern languages, the mentioned type of moving (the heart) is called

motivat-ing; both terms go back to the same Latin root.

Galilean physics, heat and electricity Adventures: sport, music, sailing, cooking,

describing beauty and understanding its origin (vol I ), using electricity, light and computers, understanding the brain and people (vol III ).

Special relativity Adventures: light,

magnetism, length contraction, time dilation and

E 0 = mc2 (vol II).

Quantum theory Adventures: death,

reproduction, biology, chemistry, evolution, enjoying colours and art, all high-tech business, medicine (vol IV and V ).

Quantum theory with gravity

Adventures: bouncing

neutrons, standing tree growth (vol V ).

under-Final, unified description of motion

Adventures: understanding

motion, intense joy with thinking, calculating couplings and masses, catching

with the least action principle.

Quantum field theory Adventures: building

accelerators, standing quarks, stars, bombs and the basis of

under-life, matter, radiation

(vol V ).

How do everyday, fast and large things move?

How do small things move?

What are things?

Why does motion occur? What are space, time and quantum particles?

General relativity

Adventures: the

night sky,

measu-ring curved space,

F I G U R E 1 A complete map of physics: the connections are defined by the speed of light c, the

gravitational constant G, the Planck constant h, the Boltzmann constant k and the elementary charge e.

Advice for learners

In my experience as a teacher, there was one learning method that never failed to form unsuccessful pupils into successful ones: if you read a book for study, summarize

trans-every section you read, in your own images and words, aloud If you are unable to do

so, read the section again Repeat this until you can clearly summarize what you read inyour own images and words, aloud You can do this alone in a room, or with friends, orwhile walking If you do this with everything you read, you will reduce your learning andreading time significantly

The most inefficient learning method is to use a marker or to underline text: it wastestime, provides false comfort and makes the text unreadable Nobody marking text is an

efficient learner Instead, by repeating every section in your own images and words, aloud,you will save time and money, enjoy learning from good texts much more and hate badtexts much less Masters of the method can use it even while listening to a lecture, in alow voice, thus avoiding to ever take notes.

Using this book

Text in green, as found in many marginal notes, marks a link that can be clicked in a pdfreader Such green links are either bibliographic references, footnotes, cross references

to other pages, challenge solutions, or pointers to websites

Solutions and hints for challenges are given in the appendix Challenges are classified

as research level (r), difficult (d), standard student level (s) and easy (e) Challenges oftype r, d or s for which no solution has yet been included in the book are marked (ny)

Feedback and support

This text is and will remain free to download from the internet I would be delighted toreceive an email from you at fb@motionmountain.net, especially on the following issues:

— What was unclear and should be improved?

Challenge 1 s

— What story, topic, riddle, picture or movie did you miss?

— What should be corrected?

In order to simplify annotations, the pdf file allows adding yellow sticker notes inAdobe Reader Alternatively, you can provide feedback onwww.motionmountain.net/wiki Help on the specific points listed on thewww.motionmountain.net/help.htmlwebpage would be particularly welcome All feedback will be used to improve the next edi-tion On behalf of all readers, thank you in advance for your input For a particularlyuseful contribution you will be mentioned – if you want – in the acknowledgements,receive a reward, or both

Your donation to the charitable, tax-exempt non-profit organisation that produces,translates and publishes this book series is welcome! For details, see the web pagewww.motionmountain.net/donation.html If you want, your name will be included in thesponsor list Thank you in advance for your help, on behalf of all readers across the world

A paper edition of this book, printed on demand and delivered by mail to any dress, can be ordered atwww.lulu.com/spotlight/motionmountain But above all, enjoythe reading!

14 1 L iquid electricit y, invisible fields and maximum speed

Fields: amber, lodestone and mobile phones 15 • How can one make lightning? 16

• Electric charge 20 • Electric field strength 23 • Pumping charge 27 • What

is electricity? 28 • Can we detect the inertia of electricity? 28 • Feeling electric fields 30 • Magnets and other magnetic materials 32 • Can humans feel magnetic fields? 35 • Magnetism and electricity 37 • How can one make a motor? 38

• Which currents flow inside magnets? 40 • Magnetic fields 41 • netism 43 • The invariants and the Lagrangian of electromagnetic fields 45 • The uses of electromagnetic effects 46 • How motors prove relativity to be right 46 • Curiosities and fun challenges about things electric and magnetic 48 • Hopping electrons and the biggest disappointment of the television industry 65 • How do nerves work? 66 • A summary: three basic facts about electricity 68

The first field equation of electrodynamics 70 • The second field equation of trodynamics 71 • The validity and the essence of Maxwell’s field equations 73 • Colliding charged particles 73 • The gauge field – the electromagnetic vector poten- tial 74 • Energy and momenta of the electromagnetic field 79 • The Lagrangian

elec-of electromagnetism 79 • The energy–momentum tensor and its symmetries of motion 81 • What is a mirror? 82 • What is the difference between electric and magnetic fields? 83 • Could electrodynamics be different? 84 • The brain: the toughest challenge for electrodynamics 85 • Challenges and fun curiosities about electrodynamics 87 • Summary 88

What are electromagnetic waves? 90 • Light as an electromagnetic wave 93 • Polarization and electromagnetic waves 95 • Light and other electromagnetic waves 99 • The slowness of progress in physics 102 • Another look at electromag- netic radiation 103 • How does the world look when riding on a light beam? 105

• Can one touch light? 106 • War, light and lies 110 • What is colour? 110 • Fun with rainbows 113 • What is the speed of light? – Again 115 • Signals and predic- tions 118 • Aether good-bye 119 • Challenges and fun curiosities about light 120

• Summary on light 122

Ways to produce images 123

Why can we see each other? Black bodies and the temperature of light 125 • Limits

to the concentration of light 128 • Measuring light intensity 129 • Other light and radiation sources 131 • Radiation as weapon 131

Making images with mirrors 133 • Does light always travel in a straight line? – Refraction 133 • Bending light with tubes – fibre optics 140 • 200 years too late – negative refraction indices 140 • Metamaterials 141 • Light around corners – diffraction 142 • Beating the diffraction limit 144 • Other ways to bend light 145 • How does one make holograms and other three-dimensional images? 147 • Images through scanning 150 • Tomography 153

Do we see what exists? 154 • How can one make pictures of the inside of the eye? 157 • How to prove you’re holy 159 • Challenges and fun curiosities about images and the eye 159 • Summary on optics 168

Strong fields and gravitation 194 • Charges are discrete 194 • How fast do charges move? 195 • Challenges and curiosities about charge discreteness 196

Evolution 200 • Children, laws and physics 200 • Polymer electronics 203 • Why a brain? 203 • What is information? 208 • What is memory? 209 • The capacity of the brain 212 • Curiosities about the brain 214

What is language? 218 • What is a concept? 222 • What are sets? What are relations? 224 • Infinity 226 • Functions and structures 228 • Numbers 229

• Why use mathematics? 234 • Is mathematics a language? 234 • Curiosities and fun challenges about mathematics 235

Are physical concepts discovered or created? 240 • How do we find physical patterns and rules? 242 • What is a lie? 243 • What is a good lie? 244

• Is this statement true? – A bit about nonsense 248 • Curiosities and fun challenges about lies and nonsense 249

Have enough observations been recorded? 253 • Are all physical observables known? 254 • Do observations take time? 256 • Is induction a problem in physics? 257

What are interactions? – No emergence 259 • What is existence? 260 • Do things exist? 261 • Does the void exist? 262 • Is nature infinite? 263 • Is the universe a set? 264 • Does the universe exist? 266 • What is creation? 266

• Is nature designed? 268 • What is a description? 269 • Reason, purpose and explanation 270 • Unification and demarcation 271 • Pigs, apes and the anthropic principle 272 • Does one need cause and effect in explanations? 274

• Is consciousness required? 275 • Curiosity 275 • Courage 277

What can move? 280 • Properties of classical motion 281 • The future of planet Earth 282 • The essence of classical physics – the infinitely small and the lack of surprises 284 • Why have we not yet reached the top of the mountain? 285

SI units 287 • The meaning of measurement 290 • Precision and accuracy of surements 290 • Limits to precision 292 • Physical constants 292 • Useful num- bers 300

In our quest to learn how things move,

the experience of hiking and other motion

leads us to discover that images are produced by charges,that charges move, accumulate and interact,

and that there is a smallest charge in nature

We understand what love has to do with magnets and amber,why the brain is such an interesting device,

and what distinguishes a good from a bad lie

L IQUI D E L E C T R IC I T Y, I N V I SI BLE

FIELDS AND MA XIMUM SPEED

What is light? The study of relativity left us completely in the dark, even though

e had embarked in it precisely to find an answer to that question True,

e have learned how the motion of light compares with that of objects Wealso learned that light is a moving entity that cannot be stopped, that light provides thespeed limit for any type of energy, and that light is our measurement standard for speed.However, we haven’t learned anything about the nature of light itself

A second question is open: what is contact? We still do not know The only thing we

learned in our exploration of relativity was that truly mechanical interactions do not exist

Vol II, page 76 Indeed, all interactions are due to exchange of particles But which ones?

The answer to the questions about the nature of light and contact emerges only from

the study of those types of motion that are not related to gravitation It turns out that the

key to the answers is the understanding of the ways magicians levitate objects

If we make a list of motors found in this world,

de-scribes any type of motor Neither the motion of sea waves, fire and earthquakes, northat of a gentle breeze is caused by gravity The same applies to the motion of muscles.*Have you ever listened to your own heart beat with a stethoscope?

med-ical doctors do now, anMP3player to record your heart beat.) Without having done so,you cannot claim to have experienced the mystery of motion Your heart has about 3000million beats in your lifetime Then it stops

It was one of the most astonishing discoveries of science that heart beats, sea wavesand most other cases of everyday motion, as well as the nature of light itself, are con-nected to observations made thousands of years ago using two strange stones These

stones show that all those examples of motion that are called mechanical in everyday life are, without exception, of electrical origin.

In particular, the solidity, the softness and the impenetrability of matter are due tointernal electricity; also the emission of light is an electrical process

are part of everyday life, we will leave aside all complications due to gravity and curvedspace-time The most productive way to study electrical motion is to start, as in the case

of gravity, with those types of motion which are generated without any contact betweenthe bodies involved

* The photograph of a circular rainbow on page 13 was taken in 2006 from the Telstra Tower in Canberra (© Oat Vaiyaboon).

F I G U R E 2 Objects surrounded by fields: amber (c 1 cm), lodestone (c 1 cm) and mobile phone

(c 10 cm) (© Philips).

water pipe

comb rubbed

on wool

F I G U R E 3 How to amaze kids, especially in dry weather (photo © Robert Fritzius).

Fields: amber, lodestone and mobile phones

The story of electricity starts with trees Trees have a special relation to electricity When

a tree is cut, a viscous resin appears With time it solidifies and, after millions of years, it

forms amber When amber is rubbed with a cat fur, it acquires the ability to attract small

objects, such as saw dust or pieces of paper This was already known to Thales of Miletus,one of the original seven sages, in the sixth century bce The same observation can bemade with many other polymer combinations, for example with combs and hair, withsoles of the shoe on carpets, and with a television tube and dust Children are always sur-prised by the effect, shown inFigure 3, that a comb rubbed on wool has on running tapwater The same effect can be produced with an air-filled rubber balloon rubbed on wool.Another interesting effect can be observed when a rubbed comb is put near a burningcandle (Can you imagine what happens?)

Challenge 3 ny

Another part of the story of electricity involves lodestone, an iron mineral found in

cer-tain caves around the world, e.g in a region (still) called Magnesia in the Greek province

of Thessalia, and in some regions in central Asia When two stones of this mineral are putnear each other, they attract or repel each other, depending on their relative orientation

In addition, lodestone attracts objects made of cobalt, nickel or iron

Today we also find various small objects in nature with more sophisticated properties,such as the one shown on the right ofFigure 2 Some of these objects allow you to talk

with far away friends, others unlock car doors, still others enable you to switch on atelevision.

All these observations show that in nature there are situations where bodies exert

in-fluence on others at a distance The space surrounding a body exerting such an inin-fluence

is said to contain a field A (physical) field is thus an entity that manifests itself by erating other bodies in a given region of space A field is space that changes momenta If you prefer, a field is space that exerts forces Or again, a field is space with some extra

accel-structure Despite this extra structure, fields, like space, are invisible

The field surrounding the mineral found in Magnesia is called a magnetic field and the stones are called magnets.

root meaning ‘brilliant, shining’ – is called an electric field The name is due to a proposal

by the famous English physician and part-time physicist William Gilbert (1544–1603)

Objects surrounded by a permanent electric field are called electrets Electrets are much

less common than magnets; among others, they are used in certain loudspeaker systems

The field around a mobile phone is called a radio field or, as we will see later, an tromagnetic field In contrast to the previous fields, it oscillates over time We will find

elec-out later that many other objects are surrounded by such fields, though these are oftenvery weak Objects that emit oscillating fields, such as mobile phones, are called radiotransmitters or electromagnetic emitters

Experiments show that fields have no mass Without any material support, fields

influ-ence bodies over a distance Fields are invisible To make them imaginable, we just need

to colour them Some ways to colour electric fields are shown inFigure 4 These figures

are the best way to imagine electric fields: they reproduce faithfully how the inventor of

the field concept, Michael Faraday, imagined them

For a long time, electric, magnetic and radio fields were rarely noticed in everydaylife Indeed, in the past, most countries had laws that did not allow producing such fields

or building mobile phones or garage openers Still today, laws severely restrict the erties of machines that use and produce such fields The laws require that for any device

prop-that moves, produces sound, or creates moving pictures, fields need to remain inside the

device For this reason a magician moving an object on a table via a hidden magnet stillsurprises and entertains his audience To feel the fascination of fields more strongly, adeeper look into a few experimental results is worthwhile

How can one make lightning?

Everybody has seen a lightning flash or has observed the effect it can have on striking atree Obviously lightning is a moving phenomenon Photographs such as that ofFigure 5show that the tip of a lightning flash advance with an average speed of around 600 km/s

But what is moving? To find out, we have to find a way of making lightning for ourselves.

In 1995, the car company General Motors accidentally rediscovered an old and simplemethod of achieving this

Opel engineers had inadvertently built a spark generating mechanism into their cars;when filling the petrol tank, sparks were generated, which sometimes lead to the explo-sion of the fuel at the petrol station

F I G U R E 4 Visualizing what is invisible: a simple way to visualize electric fields as space with a structure, using computer graphics and using seeds in oil Top: the field around a point or spherical charge;

second row: two or three charges of different signs; third row: two charges of the same sign; bottom: a charge in an external field E, and the field between two plates The charge will feel a force F directed

along the so-called electric field lines; the density of the lines gives the intensity of the field and thus the

strength of the force (© MIT, Eli Sidman, MIT).

F I G U R E 5 Lightning: a picture taken with a moving camera, showing its multiple strokes (© Steven Horsburgh).

a electrical device which anyone can build at home and which was originally invented

by William Thomson:*the Kelvin generator Repeating his experiment today, we would

take two water taps, four empty bean or coffee cans, of which two have been opened atboth sides, some nylon rope and some metal wire

Figure 6, and letting the water flow, we find a strange effect: large sparks periodicallyjump between the two copper wires at the point where they are nearest to each other,giving out loud bangs Can you guess what condition for the flow has to be realized forthis to work? And what did Opel do to repair the cars they recalled?

Challenge 4 s

If we stop the water flowing just before the next spark is due, we find that both bucketsare able to attract sawdust and pieces of paper The generator thus does the same thatrubbing amber does, just with more bang for the buck(et) Both buckets are surrounded

by electric fields The fields increase with time, until the spark jumps Just after the spark,the buckets are (almost) without electric field Obviously, the flow of water somehow

collects something on each bucket; today we call this electric charge Charge can flow

in metals and, when the fields are high enough, through air We also find that the two

buckets are always surrounded by two different types of electric fields: bodies that are

attracted by one bucket are repelled by the other

The discovery that there are two different types of electric charge is due to the French

universal genius Charles Dufay (1698–1739) In a long and careful series of experiments

* William Thomson (1824–1907), important Irish Unionist physicist and professor at Glasgow University.

He worked on the determination of the age of the Earth, showing that it was much older than 6000 years,

as several sects believed, but also (falsely) maintained that the Earth was much younger than geologists and Darwin (correctly) hat deduced He strongly influenced the development of the theory of magnetism and electricity, the description of the aether, and thermodynamics He propagated the use of the term ‘energy’

as it is used today, instead of the confusing older terms He was one of the last scientists to propagate chanical analogies for the explanation of phenomena, and thus strongly opposed Maxwell’s description of electromagnetism It was mainly for this reason that he did not receive a Nobel Prize He was also one of the minds behind the laying of the first transatlantic telegraphic cable Victorian and religious to his bones, when he was knighted, he chose the name of a small brook near his home as his new name; thus he became Baron Kelvin of Largs Therefore the unit of temperature obtained its name from a small Scottish river.

he confirmed that all materials he could get hold of can be charged electrically, and that

all charges can be classified into two types He was

bod-ies of the same charge repel each other, and that bodbod-ies of different charge attract each

other He showed in detail that all experiments on electricity can be explained with thesestatements Dufay called the two types of charges ‘vitreous’ and ‘resinous’ Unfortunately,Dufay died at a young age Nevertheless, his results spread quickly A few years later,Georg Bose used them to develop the first electrifying machine, which then made theexploration of sparks and the science of electricity fashionable across Europe.*

Twenty years after Dufay, in the 1750s, the US politician and part-time physicist jamin Franklin (1706–1790) proposed to call the electricity created on a glass rod rubbed

Ben-with a dry cloth positive instead of vitreous, and that on a piece of amber negative instead

of resinous Thus, instead of two types of electricity, he proposed that there is really onlyone type, and that bodies can either have too much or too little of it With the new terms,bodies with charges of the same sign repel each other, bodies with opposite charges at-tract each other; charges of opposite sign flowing together cancel each other out Largeabsolute values of charge imply large charge effects It took over a hundred years beforethese concepts were accepted unanimously

Electric effects are due to the flow of charges Now, all flows take time How fast iselectricity? A simple way to measure the speed of electricity is to produce a small spark

at one end of a long metal wire, and to observe how long it takes until the spark appears

at the other end of the wire In practice, the two sparks are almost simultaneous; thespeed one measures is much higher than everything else we observe in our environment.How can we measure the time nevertheless? And why did different researchers get very

* In fact, the fashion still goes on Today, there are many additional ways to produces sparks or even arcs, i.e., sustained sparks There is a sizeable subculture of people who build such high voltage generators as a hobby at home; see the www.kronjaeger.com/hv website There is also a sizeable subculture of people who

do this professionally, paid by tax money: the people who build particle accelerators.

different speed values in this experiment?

Challenge 5 s

Sparks, electric arcs and lightning are similar Of course, one has to check whether ural lightning is actually electrical in origin In 1752, experiments performed in France,following a suggestion by Benjamin Franklin, published in London in 1751, showed thatone can indeed draw electricity from a thunderstorm via a long rod.* Thunderstormclouds are surrounded by electric fields These French experiments made Franklin fam-ous worldwide; they were also the start of the use of lightning rods all over the world.Later, Franklin had a lightning rod built through his own house,

un-usual type, as shown inFigure 7 This device, invented by Andrew Gordon, is called an

electric chime Can you guess what it did in his hall during bad weather, all parts being

made of metal, and why?

light-ning rod can kill.)

In summary, electric fields start at bodies, provided they are charged Charging can

be achieved by rubbing and other processes There are two types of charge, negative and

positive Charge can flow: it is then called an electric current The worst conductors of current are polymers; they are called insulators or dielectrics A charge put on an insulator

remains at the place where it was put In contrast, metals are good conductors; a chargeplaced on a conductor spreads all over its surface The best conductors are silver andcopper This is the reason that at present, after two hundred years of use of electricity, thehighest concentration of copper in the world is below the surface of Manhattan

Electric charge

If all experiments with charge can be explained by calling the two charges positive andnegative, the implication is that some bodies have more, and some less charge than an

uncharged, neutral body Electricity thus only flows when two differently charged bodies

are brought into contact Now, if charge can flow and accumulate, we must be able to

somehow measure its amount Obviously, the amount of electric charge on a body, ally abbreviated q, must be defined via the influence the body, say a piece of sawdust, feels

usu-* The details of how lightning is generated and how it propagates are still a topic of research An introduction

F I G U R E 8 A simple set-up to confirm electric charge conservation: if rubbed fur is moved from the first pot to the second, the charge taken away from the first pot is transferred to the second, as shown by the two electrometers (© Wolfgang Rueckner).

when subjected to a field Charge is thus defined by comparing it to a standard reference

charge For a charged body of mass m accelerated in a field, its charge q is determined by

In practice, electric charge is measured with electrometers A few such devices are

shown inFigure 9 The main experimental properties of electric charge that are ered when experimenting with electrometers are listed inTable 1 In all details, chargebehaves like a flowing substance; charge behaves like a fluid

discov-Nowadays the unit of charge, the coulomb, is defined through a standard flow through

metal wires, as explained inAppendix A This is possible because all experiments show

that charge is conserved, that it flows, and thus that it can accumulate In other words, if

the electric charge of a physical system changes, the reason always is that charge is flowinginto or out of the system This can be checked easily with two metal pots connected

to two electrometers, as shown inFigure 8

Therefore we are forced to use for its description a scalar quantity q, which can take

positive, vanishing, or negative values

Describing charge as a scalar quantity reproduces the behaviour electrical charge inall everyday situations However, as in the case of all previously encountered classicalconcepts, some of the experimental results for electrical charge in everyday situationswill turn out to be only approximate More precise experiments will require a revision ofthe idea of continuous change of charge value However, the main observation remains:

no counter-example to charge conservation has as yet been observed

Objects without electric charge are called neutral A charged object that is brought

F I G U R E 9 Various electrometers: a self-made electrometer based on a jam pot, an ancient (opened)

high precision Dolezalek electrometer, the Ampullae of Lorenzini of a shark, and a modern digital

electrometer (© Harald Chmela, Klaus Jost at www.jostimages.com , Advantest).

TA B L E 1 Properties of classical electric charge: a scalar density.

near a neutral body polarizes it Electrical polarization is the separation of the positive

and negative charges in a body For this reason, all neutral objects, such as hair, are tracted to a charged body, such as a rubbed comb Generally, both insulators and con-ductors can be polarized; polarization occurs for single molecule up to whole stars

TA B L E 2 Values of electrical charge observed in nature.

C Total charge of positive (or negative) sign observed in universe 1060±1C

Electric field strength

Charges produce attraction and repulsion on other charges Equivalently, charges changemomenta; charges exert forces on other charges This happens over large distances Ex-periments that explore energy and momentum conservation show that the best descrip-tion of these interactions is as told so far: a charge produces a field, the field then acts on

a second charge

Experiments show that the electric field forms lines in space As a consequence, the

electric field behaves like a small arrow fixed at each point x in space Electric fields are

described by a direction and a magnitude The local direction of the field is given by thelocal direction of the field line – the tangent of the field line The local magnitude of thefield is given by the local density of the field lines The direction and the magnitude do

not depend on the observer In short, the electric field E(x) is a vector field Experiments

show that it is best defined by the relation

qE (x) = dp (x)

taken at every point in space x The definition of the electric field is thus based on how

it moves charges In general, the electric field is a vector

By the way, does the definition of electric field just given assume a charge speed that

is much less than that of light?

TA B L E 3 Some observed electric fields.

Field of a 100 W FM radio transmitter at 100 km distance 0.5 mV/m

Maximum practical electric field in vacuum, limited by electron

pair production

1.3 EV/m Maximum possible electric field in nature (corrected Planck elec-

62 V/m

To describe the motion due to electricity completely, we need a relation explaining

how charges produce electric fields This relation was established with precision (but not

for the first time) during the French Revolution by Charles-Augustin de Coulomb, onhis private estate.*He found that around any small-sized or any spherical charge Q at

rest there is an electric field At a position r, the electric field E is given by

Later we will extend the relation for a charge in motion The bizarre proportionality

con-stant, built around the so-called permittivity of free space ε0, is due to the historical waythe unit of charge was defined first.**The essential point of the formula is the decrease of

* Charles-Augustin de Coulomb (b 1736 Angoulême, d 1806 Paris), French engineer and physicist His careful experiments on electric charges provided a firm basis for the study of electricity.

** Other definitions of this and other proportionality constants to be encountered later are possible,

leading to unit systems different from the SI system used here The SI system is presented in detail in

Appendix A Among the older competitors, the Gaussian unit system often used in theoretical calculations, the Heaviside–Lorentz unit system, the electrostatic unit system and the electromagnetic unit system are the most important

R A

2R

4A

3R

9A

F I G U R E 10 A visualization of Coulomb’s formula and Gauss’ law.

the field with the square of the distance; can you imagine the origin of this dependence?

Challenge 10 s A simple way to picture Coulomb’s formula is illustrated inFigure 10

The two previous equations allow us to write the interaction between two chargedbodies as

where dp is the momentum change, and r is the vector connecting the two centres

of mass This famous expression for electrostatic attraction and repulsion, also due toCoulomb, is valid only for charged bodies that are either of small size or spherical, and

most of all, only for bodies that are at rest with respect to each other and to the observer This description defines the field of electrostatics.

Electric fields accelerate charges As a result, in everyday life, electric fields have twomain properties: they contain energy and they can polarize bodies The energy content

is due to the electrostatic interaction between charges The strength of this interaction isconsiderable For example, it is the basis for the force of our muscles Muscular force is

a macroscopic effect of Coulomb’s relation (5) Another example is the material strength

of steel or diamond As we will discover, all atoms are held together by electrostatic traction To convince yourself of the strength of electrostatic attraction, answer the fol-lowing: What is the force between two boxes with a gram of protons each, located on thetwo poles of the Earth? Try to guess the result

Coulomb’s relation for the field around a charge can be rephrased in a way that helps

to generalize it to non-spherical bodies Take a closed surface, i.e., a surface than encloses

a certain volume Then the integral of the electric field over this surface, the electric flux,

TA B L E 4 Properties of the classical electric field: a (polar) vector at every point in space.

page 336

dimensionality

Vol I, page 77

Change direction under

reflection

Keep direction under time

This mathematical relation, called Gauss’s ‘law’,*from the result of Coulomb

in the simplified form given here, it is valid only for static situations.) Since inside

con-ductors the electrical field is zero, Gauss’s ‘law’ implies, for example, that if a charge q is surrounded by an uncharged metal sphere, the outer surface of the metal sphere shows the same charge q.

Challenge 13 e

Do uncharged bodies attract one other? In first approximation they do not But whenthe question is investigated more precisely, we will find

* Carl-Friedrich Gauß (b 1777 Braunschweig, d 1855 Göttingen), German mathematician He was together with the Leonhard Euler, the most important mathematician of all times A famous enfant prodige, when

he was 19 years old, he constructed the regular heptadecagon with compass and ruler (see www.mathworld wolfram.com/Heptadecagon.html ) He was so proud of this result that he put a drawing of the figure on his tomb Gauss produced many results in number theory, topology, statistics, algebra, complex numbers and differential geometry which are part of modern mathematics and bear his name Among his many accom- plishments, he produced a theory of curvature and developed non-Euclidean geometry He also worked on electromagnetism and astronomy.

Gauss was a difficult character, worked always for himself, and did not found a school He published little, as his motto was: pauca sed matura As a consequence, when another mathematician published a new result, he regularly produced a notebook in which he had noted the very same result already years before His notebooks are now available online at www.sub.uni-goettingen.de

F I G U R E 11 Various types of charge pumps: a bicycle dynamo, an alternator in a power station, a

Wimshurst machine, an electric eel, a voltaic cell, a leaf and a solar cell (© Wikimedia, Q-Cells).

Can you find the conditions for this to happen?

impor-tant, as our own bodies, which are made of neutral molecules, are held together in thisway

Pumping charge

Owing to the high strength of electromagnetic interactions, separating charges is not aneasy task This is the reason that electrical effects have only been commonly used forabout a hundred years Humanity had to wait for practical and efficient devices to beinvented for separating charges and putting them into motion: to use electric effects, we

need charge pumps Some types are shown inFigure 11

Of course, every charge pump requires energy Batteries in mobile phones and the ionchannels in living cells use chemical energy to do the trick Thermoelectric elements, asused in some watches, use the temperature difference between the wrist and the air toseparate charges; solar cells use light, and dynamos or Kelvin generators use kinetic en-

If electric charge in metals moves

like a fluid, it should:

fall under gravity

The answer to this question is: Electricity is the name for a field of inquiry, but not the

name for any specific observation or effect Electricity is not a specific term; sometimes it

is used to refer to electric current and its effects, sometimes to observations about of tric charge, sometimes to the effects of electric fields In fact the vocabulary issue hides

elec-a deeper question thelec-at remelec-ains unelec-answered elec-at the end of the twentieth century: whelec-at

is the nature of electric charge? In order to solve this issue, we start with the followingquestion

Can we detect the inertia of electricity?

If electric charge really is something flowing through metals, we should be able to

ob-serve the effects shown inFigure 12: electric charge should fall, should have inertia andshould be separable from matter Indeed, each of these effects has been observed Forexample, when a long metal rod is kept vertically, we can measure an electrical potentialdifference, a voltage, between the top and the bottom In other words, we can measure

the weight of electricity in this way Similarly, we can measure the potential difference

between the ends of an accelerated rod

dif-ference between the centre and the rim of a rotating metal disc The last experiment was,

in fact, the way in which the ratio q/m for currents in metals was first measured with

precision The result is

for all metals, with small variations in the second digit The minus sign is due to thedefinition of charge In short, electrical charge in metals has mass, though a very smallone

If electric charge has mass, whenever we switch on an electrical current, we get a recoil.

This simple effect can easily be measured

Also, the emission of current into air or into vacuum is observed; in fact, every televisiontube uses this principle to generate the beam producing the picture It works best formetal objects with sharp, pointed tips

are ‘free’ electricity – are called cathode rays Within a few per cent, they show the same

mass to charge ratio as expression (7) This correspondence thus shows that charges movealmost as freely in metals as in air; this is the reason that metals are such good conductors

If electric charge falls inside vertical metal rods, we can make the astonishing

deduc-tion that cathode rays – as we will see later, they consist of free electrons*– should not

be able to fall through a vertical metal tube This is due to exact compensation of theacceleration by the electrical field generated by the displaced electricity in the tube andthe acceleration of gravity Thus electrons should not

cylinder This would not be the case if electricity in metals did not behave like a fluid Theexperiment has indeed been performed, and a reduction

for electrons of 90 % has been observed Can you imagine why the ideal value of 100 %

By noting how much the three spark images were shifted against each other on a screen,

he determined the speed to be 0.45 Gm/s, though with a large error Latter, more precisemeasurements showed that the speed is always below 0.3 Gm/s, and that it depends onthe metal and the type of insulation of the wire The high value of the speed convincedmany people to use electricity for transmitting messages In fact, these experiments mea-sure the signal speed of electromagnetic waves carried by metal wires For the actualspeed of electric charges, see below

for computer fans, uses the ‘ping’ command from theUNIXoperating system The ‘ping’

* The name ‘electron’ is due to George Stoney Electrons are the smallest and lightest charges moving in metals; they are, usually – but not always – the ‘atoms’ of electricity – for example in metals Their charge

is small, 0.16 aC, so that flows of charge typical of everyday life consist of large numbers of electrons; as a result, electrical charge behaves like a continuous fluid The particle itself was discovered and presented in

1897 by the Prussian physicist Johann Emil Wiechert (1861–1928) and, independently, three months later,

by the British physicist Joseph John Thomson (1856–1940).

TA B L E 5 Some observed electric current values.

Smallest current ever measured (for one moving electron)

3 aA

100 mA

Current inside the Earth, at the origin of its magnetic field

c.100 MA Maximum possible current in nature (cor-

rected Planck electric currente󵀆c5/4ħG )

1.5 YA

command

re-turn back If the cable length between two computers is known, the signal speed can bededuced Just try

Challenge 18 e

As a note, the speed of electricity is too slow for many people Modern computers that

are connected to stock exchanges are located as near as possible to the stock exchange,because the time advantage the short communication distance provides is essential forgetting a good financial performance in certain trading markets

We will meet these particles later in our adventure

In summary, experiments show that all charges have mass And like all massive bodies,charges move slower than light Charge is a property of matter; images and light have nocharge

Feeling electric fields

Why is electricity dangerous to humans? The main reason is that the human body is trolled by ‘electric wires’ itself As a result, electricity applied to human bodies from theoutside interferes with the internal signals This has been known since 1789 In that yearthe Italian medical doctor Luigi Galvani (1737–1798) discovered that electrical currentmakes the muscles of a dead animal contract The famous first experiment used froglegs: when electricity was applied to them, they twitched violently Subsequent investiga-tions confirmed that all nerves make use of electrical signals Using electricity, one canmake fresh corpses move, for example Nerves are the ‘control wires’ of animals We will

TA B L E 6 Some sensors for electrical current.

Conventional 20 euro multimeter voltage drop over resistor up to c.3 A

Reversible muscle contraction

some damage

times, or up to 1 A for at most 200 ms

explore nerves in more detail below

Page 66

Being electrically controlled, all mammals can sense strong electric fields Humanscan sense fields as low as 10 kV/m, when hair stands on end In contrast, several animalscan sense much weaker electric (and magnetic) fields Sharks, for example, can detectfields down to 1 μV/m using special sensors, the Ampullae of Lorenzini, which are foundaround their mouth Sharks use them to detect the field created by prey moving in wa-ter; this allows them to catch their prey even in the dark Several freshwater fish, thesalamander and the platypus, the famous duck-billed mammal, can also sense electricfields

see through Certain fish, the so-called weakly-electric fish, even generate a weak field

in order to achieve better prey detection.*In fact, several electric fish use time-varyingelectric dipole fields to communicate! They tell each other their species, their sex, theiridentity, and communicate about courtship, aggression, appeasement and dangers

frequencies they use are in the range between a few and 200 Hz, and the fields are dipolefields created between the anterior and posterior sections of their bodies

No land animal has special sensors for electric fields, because any electric field in air

is strongly damped when it encounters a water-filled animal body.**Indeed, the usualatmosphere has a low, vertical electric field of around 100 V/m; inside the human bodythis field is damped to the μV/m range, which is much less than an animal’s internalelectric fields In other words, humans do not have sensors for low electric fields becausethey are land animals (Do humans have the ability to sense electric fields in water? No-body seems to know.)

people can sense approaching thunderstorms in their joints This is due the coincidence

* It took until the year 2000 for technology to make use of the same effect Nowadays, airbag sensors in cars often use electric fields to sense whether the person sitting in the seat is a child or an adult, thus changing the way that the airbag behaves in an accident.

** Though a few land animas that swim a lot under water have electric field sensors.

TA B L E 7 Searches for magnetic monopoles, i.e., for magnetic charges, in over 140 experiments.

e = eZ02α = 4.1 pWb Search in minerals, from mountains to the deep ocean none, only dipoles Ref 16

between the electromagnetic field frequency emitted by thunderclouds

– and the resonant frequency of nerve cell membranes

The water content of the human body also means that the electric fields in air that arefound in nature are rarely dangerous to humans But whenever humans consciously senseelectric fields, such as when high voltage makes their hair stand on end, the situation ispotentially dangerous

The high impedance of air also means that, in the case of time-varying netic fields, humans are much more prone to be affected by the magnetic componentthan by the electric component

electromag-Magnets and other magnetic materials

The study of magnetism progressed across the world independently of the study of tricity Towards the end of the twelfth century, the compass came into use in Europe Atthat time, there were heated debates on whether it pointed to the north or the south.Then, in 1269, the French military engineer Pierre de Maricourt (1219–1292) publishedhis study of magnetic materials

magnetization, and he called them poles He found that even after a magnet is cut, the

resulting pieces always retain two poles: when the stone is left free to rotate, one points to

the north and the other to the south All magnets are dipoles The two poles are called the north pole and the south pole Like poles repel, and unlike poles attract As a consequence,

the magnetic north pole of the Earth is the one near the south pole, and vice versa.Magnets are surrounded by magnetic fields; in other terms, they are surrounded bymagnetic field lines Magnetic fields, like electric fields, can be visualized with field lines.Figure 14 shows some ways to do this We directly note the main difference betweenmagnetic and electric field lines: magnetic field lines have no beginning and no ends,they are closed The direction of the field lines gives the direction of the magentic field,and the density of the lines gives the magnitude of the field

Many systems in nature are magnets, as shown inFigure 13 The existence of twomagnetic poles is valid for all magnets in nature: molecules, atoms and elementary par-ticles are either dipoles or non-magnetic There are no magnetic monopoles Despite thepromise of eternal fame, no magnetic monopole has ever been found, as summarized inTable 7

Magnets have a second important property, shown inFigure 15: magnets transform

non-magnetic materials into magnetic ones There is thus a magnetic polarization, similar

to the electric polarization The amount of polarization depends on the material; some

F I G U R E 13 Various types of magnets and effective magnets: the needle in a compass, some horseshoe magnets, two galaxies, the magnetic organ of a dove, the Earth, a lifting magnet, and the Sun.

(© Wikimedia, Shambhavi, Anthony Ayiomamitis, NASA).

TA B L E 8 Some observed magnetic fields.

Lowest measured magnetic field (e.g., fields of the Schumann

resonances)

1 fT

Magnetic field that influences visual image quality in the dark 100 μT

Maximum static magnetic field produced with superconducting coils 22 T

Highest static magnetic fields produced in laboratory, using hybrid

magnets

45 T

Highest pulsed magnetic fields produced without coil destruction 76 T

Pulsed magnetic fields produced, lasting about 1 μs, using imploding

coils

1000 T

Highest field ever measured, on magnetar and soft gamma repeater

SGR-1806-20

0.8 to 1 ⋅ 10 11 T

Maximum possible magnetic field in nature (corrected Planck

53 T

values are given inTable 9 Certain materials, the so-called diamagnetic materials, are repelled by magnets, though usually by weak forces Others, the so-called paramagnetic materials, are attracted to magnets Some important materials, the ferromagnetic mate- rials, such as steel, retain the induced magnetic polarization: they become permanently

magnetized This happens when the atoms in the material get aligned by an external

magnet Ferromagnetic materials are used to produce permanent magnets – thus

F I G U R E 14 Visualizing magnetic fields – with computer graphics and with iron filings.

magnet

diamagnetic material

magnet

paramagnetic material

F I G U R E 15 The two basic types of magnetic material behaviour (tested in an

inhomogeneous field):

diamagnetism and paramagnetism.

cial lodestone

Note: the values of the electric permittivity depend on the frequency of the applied field and

on the temperature The values given here are only for static electric fields at room temperature Values for higher frequencies

Can humans feel magnetic fields?

“Any fool can ask more questions than seven

sages can answer.

”

Antiquity

It is known that honey bees, sharks, pigeons, the sandhill crane salmon, trout, sea tles, dolphins and certain bacteria can feel magnetic fields

magnetoreception All these life forms use this ability for navigation The most common

detection method is the use of small magnetic particles inside a cell; the cell then senseshow these small built-in magnets move in a magnetic field The magnets are tiny, typi-cally around 50 nm in size These small magnets are used to navigate along the magnetic

TA B L E 9 The magnetic properties of materials.

Paramagnetic materialsμr> 1, attracted by magnets

field of the Earth For higher animals, the variations of the magnetic field of the Earth,

20 to 70 μT, produce a landscape that is similar to the visible landscape for humans Theycan remember it and use it for navigation

In fact, migrating birds like the sandhill crane (Grus canadensis) seem to have two

ways to sense nagnetic fields The small mangetite crystals in the skin above the beakprovide a magnetic map that us used for local navigation In addition, migrating birdshave an inlination compass that tell them the angle between the magnetic field lines andthe vertical This system is based on magnetically sensitive protein molecules, so-called

cryptochromes The mechanism is located in the eye and is based on blue light This

sec-ond magnetic sense is used by birds to decide the general direction in which to fly

TA B L E 10 The dielectric properties of materials.

Barium strontium titanate (a perovskite)

500

Ferroelectric materialsεr≫ 1, able to form electrets

F I G U R E 16 The magnetotactic bacterium

Magnetobacterium bavaricum with its magnetosomes

(© Marianne Hanzlik).

devise a way to check this?

Challenge 20 r

Magnetism and electricity

Are magnetism and electricity related? In the early 19th century, François Arago*ered that they were He explored a ship that had survived a bad thunderstorm At that

discov-* François Arago (1786–1853) French physicist.

time, ships where made of wood The ship had been struck by lightning; as a result, theship needed a new compass Thus lightning has the ability to demagnetize compasses.Arago knew that lightning is an electrical phenomenon He concluded that magnetism

and electricity must be related More precisely, magnetism must be related to the motion

of electricity

If magnetism is related to motion of electricity, it must be possible to use magnetismand electricity to move matter

How can one make a motor?

“Communism is the power of the local councils

plus electricification of the whole country.

”

Lenin *The reason for Lenin’s famous statement were two discoveries One was made in 1820 byHans Christian Oersted**and the other in 1831 by Michael Faraday.***The consequences

of these experiments changed the world completely in less than one century

On the 21st of July of 1821, Hans Christian Oersted published a leaflet, in Latin, whichtook Europe by storm Oersted had found (during a lecture demonstration to his stu-dents) that when a current is sent through a wire, a nearby magnet is put into motion In

other words, he found that the flow of electricity can move bodies.

Due to Oersted’s leaflet, everybody in Europe with a bit of dexterity started to

exper-iment with electricity Further experexper-iments show that two wires in which charges flow

attract or repel each other, depending on whether the currents are parallel or lel These and other experiments show that wires in which electricity flows behave likemagnets.****In other words, Oersted had found the definite proof that electricity could

antiparal-be turned into magnetism

Shortly afterwards, Ampère*****found that coils increase these effects dramatically.

Coils behave like small magnets In particular, coils, like magnets, always have two poles,

* Lenin (b 1870 Simbirsk, d 1924 Gorki), founder of the Union of Soviet Socialist Republics, in 1920 stated this as the centre of his development plan for the country In Russian, the local councils of that time were called soviets.

** Hans Christian Oersted (1777–1851) Danish physicist.

*** Michael Faraday (b 1791 Newington Butts, d 1867 London), English physicist, was born to a simple family, without schooling, and of deep and naive religious ideas As a boy he became assistant to the most famous chemist of his time, Humphry Davy (1778–1829) He had no mathematical training, but late in his life he became member of the Royal Society A modest man, he refused all other honours in his life.

He worked on chemical topics, the atomic structure of matter and, most of all, he developed the idea of (magnetic) fields and field lines He used fields to describe all his numerous experimental discoveries about electromagnetism, such as the Faraday effect Fields were later described mathematically by Maxwell, who

at that time was the only person in Britain to take over Faraday’s field concept.

**** In fact, if one imagines tiny currents moving in circles inside magnets, one gets a unique description for all magnetic fields observed in nature.

***** André-Marie Ampère (b 1775 Lyon, d 1836 Marseille), French physicist and mathematician

Autodi-dact, he read the famous Encyclopédie as a child; in a life full of personal tragedies, he wandered from maths

to chemistry and physics, worked as a school teacher, and published nothing of importance until 1820 Then the discovery of Oersted reached all over Europe: electrical current can deviate magnetic needles Ampère worked for years on the problem, and in 1826 published the summary of his findings, which lead Maxwell

to call him the ‘Newton of electricity’ Ampère named and developed many areas of electrodynamics In

1832, he and his technician also built the first dynamo, or rotative current generator Of course, the unit of

F I G U R E 17 An old and a modern version of electric motor, and a galvonometer with limited rotation range used for steering laser beams Sizes are approximately 20 cm, 50 cm and 15 cm (© Wikimedia, Honda, Wikimedia).

usually called the north and the south pole Opposite poles attract, like poles repel eachother As is well known, the Earth is itself a large magnet, with its magnetic north polenear the geographic south pole, and vice versa However, the magnetic field of the Earth

is not due to a solid permanent magnet inside it The Earth’s solid core is too hot to be a

permanent magnet; instead, the magnetic field is due to circulating currents in the outer,liquid core (The power to keep the geodynamo running is estimated to be between 200and 500 GW and is due to the heat in the centre of the Earth.)

All the relations between electricity and magnetism can be used to make electric tors First, electric current is used to generate a magnetic field; then the field is used tomove a magnet attached to the motor axis The details on how to do this effectively de-pend on the size of the motor one is building, and form a science on its own: electricengineering.Figure 17shows some examples of electric motors

mo-electrical current is named after him.

Ampère had two cats, which he liked dearly, a large one and a small one When he was doing his ments in his laboratory, they wanted to come in, and when they were in, they soon wanted to go out One day he was fed up He made two holes in his door, a large one and a small one.

ceiling thin wire metal rod

electric current

F I G U R E 18 Current makes a metal rod rotate.

Which currents flow inside magnets?

Magnetic monopoles do not exist Therefore, all magnetic fields in nature are due to ing electric charges But that is strange: If all magnetic fields are due to the motion ofcharges, this must be also the case inside lodestone, or inside a usual permanent magnet.Can this be shown?

mov-In 1915, two men in the Netherlands found a simple way to prove that in any nent magnet, charges are moving They suspended a metal rod from the ceiling by a thinthread and then put a coil around the rod, as shown inFigure 18 They predicted thatthe tiny currents inside the rod would become aligned by the magnetic field of the coil

perma-As a result, they expected that a current passing through the coil would make the rodturn around its axis Indeed, when they sent a strong current through the coil, the rodrotated (As a result of the current, the rod was magnetized.)

the Einstein–de Haas effect after the two men who imagined, measured and explained it.*The effect thus shows that even in the case of a permanent magnet, the magnetic field isdue to the internal motion of charges The magnitude of the effect also shows that themoving particles are electrons Twelve years later it became clear that the angular mo-mentum responsible for the effect is a mixture of orbital and spin angular momentum;

in fact, the electron spin plays a central role in the effect

Permanent magnets are made from ferromagnetic materials Permanent tion is due to the alignment of microscopic rotational motions Due to this connection,

magnetiza-an even more surprising effect cmagnetiza-an be predicted: Rotating a piece of non-magnetized romagnetic material should magnetize it, because the tiny rotating currents would then

fer-be aligned along the axis of rotation

the Barnett effect after its discoverer Like the Einstein–de Haas effect, the magnitude of

the Barnett effect can also be used to determine the gyromagnetic ratio of the electron

* Wander Johannes de Haas (1878–1960), Dutch physicist De Haas is best known for two additional

magneto-electric effects named after him, the Shubnikov–de Haas effect (the strong increase of the magnetic resistance of bismuth at low temperatures and high magnetic fields) and the de Haas–van Alphen effect (the

diamagnetic susceptibility of bismuth at low temperatures is a periodic function of the magnetic field).